Robot learning is often difficult due to the expense of gathering data. The need for large amounts of data can, and should, be tackled with effective algorithms and leveraging expert information on robot dynamics. Bayesian reinforcement learning (BRL), thanks to its sample efficiency and ability to exploit prior knowledge, is uniquely positioned as such a solution method. Unfortunately, the application of BRL has been limited due to the difficulties of representing expert knowledge as well as solving the subsequent inference problem. This paper advances BRL for robotics by proposing a specialized framework for physical systems. In particular, we capture this knowledge in a factored representation, then demonstrate the posterior factorizes in a similar shape, and ultimately formalize the model in a Bayesian framework. We then introduce a sample-based online solution method, based on Monte-Carlo tree search and particle filtering, specialized to solve the resulting model. This approach can, for example, utilize typical low-level robot simulators and handle uncertainty over unknown dynamics of the environment. We empirically demonstrate its efficiency by performing on-robot learning in two human-robot interaction tasks with uncertainty about human behavior, achieving near-optimal performance after only a handful of real-world episodes. A video of learned policies is at https://youtu.be/H9xp60ngOes.